Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6 and 20 the smallest integer that is 60 that is divisible by both numbers.
Least Common Multiple (LCM) of 6 and 20 is 60.
LCM(6,20) = 60
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 20. First we will calculate the prime factors of 6 and 20.
Prime Factorization of 6
2 | 6 |
3 | 3 |
1 |
Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:
6 = 21×31
Prime Factorization of 20
2 | 20 |
2 | 10 |
5 | 5 |
1 |
Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:
20 = 22×51
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 20.
LCM(6,20) = 22×31×51
LCM(6,20) = 60
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1, 2, 3, 6
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1, 2, 4, 5, 10, 20
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 20, than apply into the LCM equation.
GCF(6,20) = 2
LCM(6,20) = ( 6 × 20) / 2
LCM(6,20) = 120 / 2
LCM(6,20) = 60
(i) The LCM of 20 and 6 is associative
LCM of 6 and 20 = LCM of 20 and 6
1. What is the LCM of 6 and 20?
Answer: LCM of 6 and 20 is 60.
2. What are the Factors of 6?
Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.
3. What are the Factors of 20?
Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.
4. How to Find the LCM of 6 and 20?
Answer:
Least Common Multiple of 6 and 20 = 60
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 20
20 = 2 x 2 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 60 = 2 x 2 x 3 x 5
Step 4: Therefore, the least common multiple of 6 and 20 is 60.